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Ann Glob Anal Geom (Dordr) 2021 1;60(3):559-587. Epub 2021 Jul 1.

Institute of Applied Mathematics, Montanuniversitaet Leoben, Peter-Tunner-Straße 25/I, 8700 Leoben, Austria.

We investigate the maximal open domain on which the orthogonal projection map onto a subset can be defined and study essential properties of . We prove that if is a submanifold of satisfying a Lipschitz condition on the tangent spaces, then can be described by a lower semi-continuous function, named . We show that this frontier function is continuous if is or if the topological skeleton of is closed and we provide an example showing that the frontier function need not be continuous in general. Read More

Ann Glob Anal Geom (Dordr) 2020 8;58(4):385-413. Epub 2020 Sep 8.

Department of Mathematics, West University of Timişoara, Bd. V.Pârvan 4, 300223 Timisoara, Romania.

A nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Fréchet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application, we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i. Read More

Ann Glob Anal Geom (Dordr) 2019 19;55(3):529-553. Epub 2018 Nov 19.

Vienna, Austria.

We study the limiting behaviour of Darboux and Calapso transforms of polarized curves in the conformal -dimensional sphere when the polarization has a pole of first or second order at some point. We prove that for a pole of first order, as the singularity is approached, all Darboux transforms converge to the original curve and all Calapso transforms converge. For a pole of second order, a generic Darboux transform converges to the original curve while a Calapso transform has a limit point or a limit circle, depending on the value of the transformation parameter. Read More

Ann Glob Anal Geom (Dordr) 2019 10;55(1):133-147. Epub 2018 Nov 10.

2Faculty of Mathematics, University of Vienna, Vienna, Austria.

We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in Kunzinger and Sämann (Ann Glob Anal Geom 54(3):399-447, 2018). To this end, we introduce appropriate notions of geodesics and timelike geodesic completeness and prove a general inextendibility result. Our results shed new light on recent analytic work in this direction and, for the first time, relate low-regularity inextendibility to (synthetic) curvature blow-up. Read More

Ann Glob Anal Geom (Dordr) 2018;53(2):283-286. Epub 2018 Feb 12.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

[This corrects the article DOI: 10.1007/s10455-016-9514-4.]. Read More

Ann Glob Anal Geom (Dordr) 2018 5;54(3):399-447. Epub 2018 Oct 5.

Faculty of Mathematics, University of Vienna, Vienna, Austria.

We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way, we recover many fundamental results in greater generality, while at the same time clarifying the minimal requirements for and the interdependence of the basic building blocks of the theory. Read More

Ann Glob Anal Geom (Dordr) 2016 7;50(3):209-235. Epub 2016 Apr 7.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

The aim of this paper is to generalize certain volume comparison theorems (Bishop-Gromov and a recent result of Treude and Grant, Ann Global Anal Geom, 43:233-251, 2013) for smooth Riemannian or Lorentzian manifolds to metrics that are only (differentiable with Lipschitz continuous derivatives). In particular we establish (using approximation methods) a volume monotonicity result for the evolution of a compact subset of a spacelike, acausal, future causally complete (i.e. Read More

Ann Glob Anal Geom (Dordr) 2016 31;50(4):347-365. Epub 2016 May 31.

Institut für diskrete Mathematik und Geometrie, TU Wien, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria.

We study harmonic maps from surfaces coupled to a scalar and a two-form potential, which arise as critical points of the action of the full bosonic string. We investigate several analytic and geometric properties of these maps and prove an existence result by the heat-flow method. Read More